Computational modelling of string-body interaction for the violin family and simulation of wolf notes

Most theoretical studies of bowed-string instruments deal with isolated strings, pinned on fixed supports. In others, the instrument body dynamics have been accounted by using extremely simplified models of the string-body interaction through the instrument bridge. Such models have, nevertheless, been instrumental to the understanding of a very common and musically undesirable phenomenon known as the wolf note-a strong beating interplay between string and body vibrations. Cellos, bad and good, are particularly prone to this problem. In previous work, a computational method that allows efficient time-domain modelling of bowed strings based on a modal approach has been introduced. This has been extended to incorporate the complex dynamics of real-life instrument bodies, and their coupling to the string motions, using experimental dynamical body data. The string is modelled using its unconstrained modes, assuming pinned-pinned boundary conditions at the tailpiece and the nut. At the intermediary bridge location, the string-body coupling is enforced using the body impulse-response or modal data, as measured at the instrument bridge. In the present paper, this computational approach is applied to a specific cello, which provided experimental wolf-behaviour data under several bowing conditions, as well as laboratory measurements of the bridge impulse responses on which the numerical simulations were based. Interesting aspects of the string-body dynamical responses are highlighted by numerical simulations and the corresponding sounds and animations produced. Finally, a qualitative (and, when possible, quantitative) comparison of the experimental and numerical results is presented. (c) 2007 Elsevier Ltd. All rights reserved.